All these conspiracy theories about Inbox seem to be using overly simplistic black and white reasoning. If Google didn't enrich emails with relevant information that users might eventually find as indispensable as a spam filter, somebody else would and steal their users, given how easy they've made it to move off their service. The jury's still out as to whether Inbox represents such an improvement, but it is obvious to me what its purpose is.
My point is that so far, everything points to Inbox falling on the "get/keep more users" side of the spectrum as opposed to the "increase monetization on existing users" side, similar to how Google Now tries to keep users giving information to Google as opposed to show them ads directly. It may eventually do both, but the former is what the current features target.